Question

V(x) കാണുക.

X	1	2	3	4	5
P(X)	K	2K	3K	2K	K

• A. 1/3
• B. 2/3
• C. 5/3
• D. 4/3

Answer 1

Answer:

D. 4/3

$V(X)=E(X^2)-[E(X)]^2$

$ΣP(X)=1$

$k+2k+3k+2k+k=1$

$9k=1$

$k=\frac{1}{9}$

$E(X)=ΣxP(x) = (1 \times k )+(2 \times 2k)+(3 \times 3k)+(4 \times 2k)+(5 \times k)$

$= k+4k+9k+8k+5k = 27k = 27 \times \frac{1}{9} = 3$

$E(X^2)= (1 \times k)+(4 \times 2k)+(9 \times 3k)+(16 \times 2k)+(25 \times k)$

$=k+8k+27k+32k+25k=93k = 93 \times \frac{1}{9} = \frac{93}{9}$

$ΣP(X)=1$

$k+2k+3k+2k+k=1$

$9k=1$

$k=\frac{1}{9}$

$V(X)= \frac{93}{9} - (3)^2 = \frac{93}{9}-9 = \frac{12}{9}= \frac{4}{3}$